Cluster mass estimation from lens magnification

Abstract

The surface mass density of a cluster of galaxies, and thus its total mass, can be estimated from its lens magnification. The magnification can be determined from the variation in number counts of its background galaxies. In the weak lensing approximation the surface mass density is a linear function of the magnification. However, most observational data are concentrated in the central parts of clusters, so one needs to go beyond the weak lensing approximation and consider the lens shear as well, which is unknown from the variation in number counts alone. Our approach is to look for approximate relations between the lens shear and other lens properties in this strong lensing regime. Such relations exist for simple analytical cluster models, like the isothermal sphere, but are not generally a good description of observed or simulated galaxy clusters. We therefore study the lensing properties of a catalogue of numerical cluster models in order to find the best possible approximation for the shear that still allows straightforward determination of the surface mass density. We show that by using such an approximation one can fairly well reconstruct the surface mass distribution from the magnification alone. The approximations are tested using clean magnification maps obtained directly from simulated clusters, and also using lensed mock background galaxy distributions in order to estimate the intrinsic uncertainties of the method. We demonstrate that the mass estimated using the weak lens magnification approximation is usually at least twice the true mass. We illustrate our technique on existing data, and show that the resulting masses compare well with other estimates.